Possibly read about a teetotaller having deserted (6)
I believe the answer is:
ratted
'deserted' is the definition.
(ratting is a kind of deserting)
'possibly read about a teetotaller' is the wordplay.
'possibly' is an anagram indicator.
'about' is an insertion indicator.
'a teetotaller' becomes 'tt' (abbreviation).
'read' with letters rearranged gives 'raed'.
'raed' enclosing 'tt' is 'RATTED'.
'having' acts as a link.
(Other definitions for ratted that I've seen before include "Betrayed or informed, the rodent" , "Broke promise in treacherous or rodent style" , "Deserted; very drunk" , "Betrayed like a rodent" , "Deserted the side, rodent-like" .)