Foresight of Trump's running mate defining Republican key initiative at the start (10)
I believe the answer is:
prescience
'foresight' is the definition.
(I've seen this before)
'trump's running mate defining republican key initiative at the start' is the wordplay.
'trump's running mate' becomes 'pence' (Donald Trump's vice president Mike Pence).
'defining' means one lot of letters goes inside another (define can mean to mark a boundary around).
'republican' becomes 'r' (abbreviation).
'key' becomes 'esc' ('Escape' key on a computer keyboard).
'at the start' says to take the initial letters.
The initial letter of 'initiative' is 'i'.
'r'+'esc'+'i'='resci'
'pence' going around 'resci' is 'PRESCIENCE'.
'of' is the link.
(Other definitions for prescience that I've seen before include "Foresight" , "knowing what will happen in future?" , "Foreknowledge" .)