Penalties extremely severe for bridge manoeuvre (7)
I believe the answer is:
Here is my best explanation:
'bridge manoeuvre' is the definition.
(term from the card game bridge)
'penalties extremely severe' is the wordplay.
'penalties' becomes 'fines' (fine is a kind of penalty).
'extremely' says to hollow out the word (remove centre letters).
'severe' with its middle taken out is 'se'.
'for' is the link.
(Other definitions for finesse that I've seen before include "Delicacy", "Subtlety of contrivance in cards", "Achieve with subtlety and skill", "Delicate manipulation, perhaps in card game", "Bridge ploy", "Subtle skill - bridge manoeuvre", "Skilful elegance or expertise", "Hopeful ploy at cards", "Refinement" and "Skill".)