There would be none, if the title 'barrister-at-law' existed ! You may 'see barrister-at-law after the name of someone online who invites you to invest in some business in Nigeria LOL. You also find it after the name of the authors of old books of the 'Everyman's own lawyer' variety. It's a peculiar affectation, either designed to impress or because the reader may not understand what 'barrister' means and 'at law' adds some explanation.
It may be modelled on serjeant-at-law, a now extinct rank of very senior barristers, or attorney-at-law, whose title needed to explain what kind of attorney he was; that may also be true of serjeant because there are , or were, other kinds of serjeant.
Anyway, someone who is 'called to the bar' is officially called 'barrister' from that moment and that remains so throughout their career.