28 across
Private
eye
capturing
Chinese
backing
popular
applied
science
(7)
Private eye capturing Chinese backing popular applied science (7)
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The definition is at the end of the clue.
How the clue works
TEC (Private eye) wraps around CH (Chinese) followed by IN (popular) reversed, indicated by "backing", giving NI. Putting it all together gives TEC around CHNI, forming TECHNIC, our applied science.