Engineers British and American puzzle (5)
I believe the answer is:
rebus
'puzzle' is the definition.
(type of visual puzzle)
'engineers british and american' is the wordplay.
'engineers' becomes 're' (Royal Engineers).
'british' becomes 'b' (abbreviation e.g. in BBC).
'and' says to put letters next to each other.
'american' becomes 'US' (abbreviation for United States).
're'+'b'+'us'='REBUS'
(Other definitions for rebus that I've seen before include "Picture-letter puzzle" , "Word puzzle with pictures and letters" , "Visual pun" , "Problem" , "Pictorial pun - fictional detective" .)