Succeed across the world and become tedious (4,4)
I believe the answer is:
wear thin
'become tedious' is the definition.
'succeed across the world' is the wordplay.
'succeed' becomes 'win' (I've seen this before).
'across' is an insertion indicator.
'the world' becomes 'earth' ('Earth' can be a synonym of 'world').
'win' enclosing 'earth' is 'WEAR THIN'.
'and' acts as a link.
(Other definitions for wear thin that I've seen before include "clothing advice for warm weather?" , "Cease to convince" , "Get less convincing" , "start to be ineffective" , "Begin to fail" .)