Teresa Danby must have been born in December of 1798 or January 1799. Her mother was 2 months pregnant when her father died in May of 1798.

from Biographical Dictionary of Actors, Actresses, Musicians, Dancers volume 4, by Philip Highfill and others.
Caroline (born 20 July 1797) and Teresa (born in January 1799) were apprenticed to another school mistress, a madame Bernard who kept “the school in the New Road near Lisson Green” and who on 6 February 1814, was said to have “left her school and deserted her apprentices.”

Transcription of Indenture, original provided by Margaret Hiles

This indenture witnesseth, That Teresa Danby aged 14 years with the consent of the Governor of the Royal Society of Musicians doth put herself Apprentice to Henrietta Bernard Schoolmistress of Charlotte Row New Road in the Parish of Marylebone County of Middlesex to learn her Art and with her after the manner of an Apprentice to serve from the date hereof unto the full End and Term of Seven Years from thence ensuing, and fully to be complete and ended, during which Term the said Apprentice her Mistress faithfully shall or will serve, her secrets keep, her lawfull Commands every where gladly do, She shall do no Damage to her said Mistress nor see it to be done to others, but to her Power shall let or forthwith give Notice to her said Mistress of the same: The Goods of her said Mistress she shall not waste; nor the same without License of her to any give or lend, hurt to her said Mistress she shall not do, cause, or procure to be done; she shall neither buy or sell without her Mistress License; Taverns, Inns, or Alehouses she shall not haunt: At Cards, Dice, Tables, or any other unlawful Games she shall not play, so that her said Mistress may be injured thereby: Nor from the Service of her said Mistress Day or Night shall absent herself, but in all things as an honest and faithful Apprentice shall and will demean and behave herself toward her said Mistress and all hers during the said Term. [I can’t believe that is 1 sentence!] And the said Henrietta Bernard in Consideration of the Sum of Twenty Five Pounds of lawful Money of Great Britain, being Charity Money allowed by the Governors of the Royal Society of Musicians, for the year of 1813 the said Apprentice in the Art of a Schoolmistress which she now useth, shall teach and instruct, or cause to be taught and instructed, in the best way and manner that she can, finding and allowing unto her said Apprentice sufficient Meat, Drink, Apparel, Washing, Lodging and all other Necessaries during the said term of Seven Years

And for the true Performance of all and every the Covenants and Agreements aforesaid, either of the said Parties bindeth themselves firmly by these Presents. In Witness whereof the Parties abovesaid to these Indentures interchangeably have set their Hands and Seals the Twenty Fifth Day of February in the Fifty Fourth Year of the Reign of our Sovereign Lord George the Third, by the Grace of God of Great Britain, France, and Ireland, King, Defender of the Faith; and in the Year of our Lord 1813

Signed, sealed and delivered in the Presence of
Mary? Jane Ashley Henrietta Bernard
Lydia Wormes?

End of indenture

Listed in the 1851 census Address 3 Dean Street Civil parish Westminster St Margaret, ecclesiastical parish Westminster, Middlesex, England. Registration District Westminster, sub registration district St Margaret.
Theresa Symondson (or Symonson) widow, head, stationer, age 51, born in London.
Son Henry Symondson age 18, born in London, occupation Music Seller.
Son Frederick Symondson age 17, born London, occupation Music Seller.
Daughter Therese Symondson, age 13, scholar, born London.
Daughter Marcella Symondson, age 9, scholar, born London.
[3 other families lived at this address as well, presumably on different floors.There are 5 floors today. I imagine their shop was on the ground floor and they lived above.]
[3 Dean Street is now a Tesco Store with address 2 to 4 Dean Street. Near Oxford Street.]
[Historical Note: Karl Marx (listed as Charles Mark) and his family were living at 28 Dean Street from 1851 to 1856]

In the 1861 census living at 10 Wellington Road West, civil parish St Pancras, ecclesiastical parish Holy Trinity, Middlesex, Registration district Pancras, sub registration district Kentish town.
Frederick Symondson age 26, letter sorter G.P.O. born at St Pancras.
Wife Catherine age 26 born at St Pancras.
Son Frederic age 5, born at St Pancras. Son Henry age 3, born at St Pancras.
Son Adolphus age 1, born at St Pancras.
Mother Teresa Symondson, widow, age 62, school mistress born at St Pancras.

Teresa Danby Symondson is listed in the 1867 April to June death index, age 68, Pancras, London, Middlesex, volume 1b page 98.

Parish Records St. Giles in The Fields, Camden, Middlesex
Baptized July 11, 1803 Henry Symondson of Henry and Mary, born 1st February.

In the 1827 Pallot’s Marriage Index Hy. Symondson bachelor Marriage to Teresa Danby spinster, St. Pancras, Middlesex.

26 FEB 1827 Old Church, Saint Pancras, London, England Teresa Danby and Henry Symondson. from IGI

From their marriage certificate:
Page 151
MARRIAGES solemnized in the Parish of Saint Pancras, in the County of
Middlesex, in the Year One Thousand Eight Hundred and Twenty
Seven.
Henry Symondson of this Parish
Bachelor
and Teresa Danby of ___(blank)_____Parish
Spinster
were married in this Church by Banns with Consent of
_____(blank)_______ this twenty sixth Day of
February in the Year One thousand eight hundred and twenty seven
By me Brackenbury Curate
This Marriage was solemnized between us Henry Symondson
Teresa Danby
In the Presence of Rich'd Brookes
Sarah Danby
No. 127

Notes about the marriage certificate.
Perhaps the consent line is blank as her father Henry Danby was deceased or perhaps she is 21 years of age.

Henry and Teresa quite likely had an older son Henry Danby Symondson who was born about 9 months after they were married, died before the 1841 census and about a year before their son Henry Symondson was born. Saint Pancras Parish Church records have a burial for Henry Danby Symondson, April 15, 1932, age 4 years 4 months. Late residence Warren Street.
Also from Parish records Saint Pancras Parish Church a Theresa Louisa Symondson, buried September 21, 1830, age 3 months. Late residence Warren Street.

In the 1839 Robson’s London and Birmingham Directory
Symondson H, mus bell founder, 20 Clipstone st.
Symondson H, cabinet piano forte mkr, 13 Robert st Hampstead rd

In the 1841 census
Civil parish St Pancras, Hundred Ossulstone (Holborn Division), Middlesex, Registration district St Pancras, sub registration district Regents Park. Living on Robert Street.
Henry Symondson age 38, pianoforte ma [maker].
Female, Teresa Symondson, age 40.
Male, Alfred Symondson, age 10,
Male Henry Symondson, age 9,
Son Frederick Symondson, age 7,
Female, Louisa Symondson, age 5,
Male [written in the wrong column] Teresa Symondson, age 3.
All were born in the county of Middlesex.

Post Office London Directory, 1841. [Part 1: Street, Commercial, & Trades Directories]
Robert Street, Hampstead Road.
13 Symondson Henry pianoforte maker
Note: There were well over 100 pianoforte makers listed in this directory!

In the 1845 Post Office Directory of London and Birmingham
Symondson Henry, pianoforte ma. 34 William st. Hampstead rd.
Symondson Philip, musical bell maker 20 1/2 Clipstone street, Fitzroy square and 1 Tottenham court road

Henry Symondson is listed in the October to December 1848 Death index, St George Southwark, Surrey, Volume 4 page 376.

Death Certificate Registration district St George the Martyr Southwark, sub district London Road Southwark, Surrey
Eleventh November 1848, 24 Gibraltar Row nr George’s Rd. Southwark. Henry Symondson, male, age 45 years, Piano forte Tuner died of Consumption (certified), informant Teresa Danby Symondson present at death 24 Gibraltar Row nr George’s Road Southwark, registered Thirteenth November 1848, A. Nedford?, Registrar

Parish record St. Mary Lambeth, Surrey
Buried November 19, 1848 Henry Symondson, abode St George’s, Southwark, age 45

The Piano Gen website lists an entry for Symondson pianos in 1840. See Internet site:
https://www.uk-piano.org/piano-gen/piano-names.html