Puzzles son with promise to split burden (10)
I believe the answer is:
crosswords
'puzzles' is the definition.
(crossword is a type of puzzle)
'son with promise to split burden' is the wordplay.
'son' becomes 's'.
'with' means one lot of letters go next to another.
'promise' becomes 'word' (as in 'I give you my word').
'to split' means one lot of letters goes inside another.
'burden' becomes 'cross' (someone's particular burden is their cross).
's'+'word'='sword'
'sword' put inside 'cross' is 'CROSSWORDS'.
(Another definition for crosswords that I've seen is " which call for solutions".)