Apprehend American’s in love (4)
I believe the answer is:
nail
'apprehend' is the definition.
(I know that apprehend can be written as nail)
'american's in love' is the wordplay.
'american' becomes 'a' (common abbreviation - e.g. in organisation names).
'in' is an insertion indicator.
'love' becomes 'nil' (love and nil mean zero in cricket and football).
'a' inserted inside 'nil' is 'NAIL'.
(Other definitions for nail that I've seen before include "metal fixture" , "Hit this on the head to be bang on" , "Hammered individual" , "Hammer's target" , "one wouldn't want in one's coffin?" .)