Beg chaps to leave maiden gift (7)
I believe the answer is:
entreat
'beg' is the definition.
(to entreat someone is to beg or plead)
'chaps to leave maiden gift' is the wordplay.
'chaps' becomes 'men' (chap means a man).
'to leave' indicates named letters should be taken away.
'maiden' becomes 'm' (cricket abbreviation).
'gift' becomes 'treat' (treating is a kind of gifting).
'men' with 'm' taken away is 'en'.
'en'+'treat'='ENTREAT'
(Other definitions for entreat that I've seen before include "Beg earnestly, implore" , "Pray" , "Ask (someone) anxiously" , "Beg earnestly or emotionally" , "petition" .)