Chap in boat having argument with Her Majesty (5)
I believe the answer is:
rower
'chap in boat' is the definition.
(someone in a rowing boat)
'argument with her majesty' is the wordplay.
'argument' becomes 'row' (to row is to argue).
'with' is a charade indicator (letters next to each other).
'her majesty' becomes 'ER' (Elizabeth Regina).
'row'+'er'='ROWER'
'having' acts as a link.
(Other definitions for rower that I've seen before include "Waterman" , "Stroke with blade" , "He handles oars" , "One in eight, perhaps" , "Oarsman (or woman)" .)