Starts to kick under new goalposts, endless fun in martial art (4,2)
I believe the answer is:
kung fu
'martial art' is the definition.
(Kung Fu is an example)
'starts to kick under new goalposts endless fun' is the wordplay.
'starts to' suggests taking the first letters.
'endless' means to remove the last letter.
The first letters of 'kick under new goalposts' is 'kung'.
'fun' with its last letter removed is 'fu'.
'kung'+'fu'='KUNG FU'
'in' is the link.
(Other definitions for kung fu that I've seen before include "Chinese form of unarmed combat, was a TV serial" , "Chinese type of karate" , "'A Chinese martial art (4,2)'" , "fighting" , "Chinese system of unarmed combat like karate" .)