Traditionally they would be written 'T. St J.', but modern practice in the British English zone is to not use periods, thus 'T St J', or possibly (less formally) 'TStJ'.
Author:Frederick Edward Molyneux St. John
This author wrote articles for the 1911 Encyclopædia Britannica.
Articles attributed to this author are designated in EB1911 by the
initials "M. St J."
Example (1)
Regarding formal style, a note to a scientific paper corrects capitalisation ('ST') and the omission of spaces:
@article{6da73ab7d99e423c9ee8fa0a2f9c9843, title = "Preparation of
core-shell polymer colloid particles by encapsulation", author = "RH
Ottewill and AB Schofield and JA Waters and NSTJ Williams", note =
"Other: 4th author - initials should read N St J (lower case t)
Williams"
Example (2)
Further, the surname, if written in full, is St John
or St. John
and (this is definitely worth knowing) in the UK, it is often pronounced 'Sinjun' or 'Sinjin'.
St John (name)