Contrary fellow and old females go out (3,3)
I believe the answer is:
nod off
'go out' is the definition.
Although both the answer and definition are verbs in their base form, I can't see how they can define each other.
'contrary fellow and old females' is the wordplay.
'contrary' says the letters should be written in reverse.
'fellow' becomes 'don' (both can mean an academic).
'and' is a charade indicator (letters next to each other).
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'females' becomes 'ff' (the abbreviation for female repeated).
'don' back-to-front is 'nod'.
'nod'+'o'+'ff'='NOD OFF'
Can you help me to learn more?
(Other definitions for nod off that I've seen before include "Fall asleep with head movements" , "Become drowsy with moving cranium" , "Go to sleep with head movements" , "Fall asleep with drooping head" , "Fall asleep casually" .)