Storm battered MEP cutting tax (7)
I believe the answer is:
tempest
'storm' is the definition.
(I know that storm can be written as tempest)
'battered mep cutting tax' is the wordplay.
'battered' indicates an anagram.
'cutting' means one lot of letters goes inside another (some letters cut their way into a word).
'tax' becomes 'test' (taxing can mean testing or demanding).
'mep' anagrammed gives 'mpe'.
'mpe' inserted inside 'test' is 'TEMPEST'.
(Other definitions for tempest that I've seen before include "Play (with rough weather)" , "Violent disturbance" , "An angry storm as in Shakespeare play" , "Outburst" , "Wild storm" .)