Philistine's tyres blown? That's hard to explain (7)
I believe the answer is:
mystery
'hard to explain' is the definition.
(I've seen this before)
'philistine's tyres blown?' is the wordplay.
'philistine's' becomes 'my' (where the crossword setter is 'Philistine').
'blown?' indicates anagramming the letters (to blow can mean to disrupt or scatter).
'tyres' with letters rearranged gives 'stery'.
'my'+'stery'='MYSTERY'
'that's' acts as a link.
(Other definitions for mystery that I've seen before include "Religious truth beyond human understanding" , "It can't be explained" , "associated with Macavity" , "Something baffling" , "thriller" .)