Beggar's right to stop one who'll cough up (6)
I believe the answer is:
prayer
'beggar's' is the definition.
(thesaurus)
'right to stop one who'll cough up' is the wordplay.
'right' becomes 'r' (abbreviation).
'to stop' indicates putting letters inside (stopping can mean blocking a gap).
'one who'll cough up' becomes 'payer' (someone who'll pay).
'r' put within 'payer' is 'PRAYER'.
(Other definitions for prayer that I've seen before include "words of church service?" , "Act of supplication to a deity" , "Litany" , "Earnest request" , "Request to deity" .)