Clue: Record set in Kane's first international cap (4)
Answer: KEPI
Explanation: Definition: cap
 EP(abbrev. for "extended play"/a disc of recorded audio material) **contained in**(set in) [ **1st letter of**(…'s first) "Kane" + I(abbrev. for "international") ].
And, in football, Harry Kane has many times been capped an England international.