American turning up with dirty bear (7)
I believe the answer is:
sustain
'bear' is the definition.
(I've seen this before)
'american turning up with dirty' is the wordplay.
'american' becomes 'us' (abbreviation for United States).
'turning up' shows that the letters should be reversed in order.
'with dirty' becomes 'stain' (I can't justify this - if you can you should give a lot more credence to this answer).
'us' in reverse letter order is 'su'.
'su'+'stain'='SUSTAIN'
Can you help me to learn more?
(Other definitions for sustain that I've seen before include "Keep (something) going" , "Endure" , "Feed, nourish" , "Withstand" , "Undergo" .)