American cut back in case of tension (5)
I believe the answer is:
texan
'american' is the definition.
(Texan is an example)
'cut back in case of tension' is the wordplay.
'cut' becomes 'axe' (I've seen this before**).
'back' says the letters should be written in reverse.
'in' means one lot of letters goes inside another.
'case of' suggests removing the centre (outsides of).
'tension' with its centre removed is 'tn'.
'axe' in reverse letter order is 'exa'.
'exa' going inside 'tn' is 'TEXAN'.
(Other definitions for texan that I've seen before include "Native of Houston, perhaps" , "like LBJ" , "Eg, native of Dallas" , "Relating to a US state" , "One from south-west USA" .)