Invites from a Conservative in backing institute with it (8)
I believe the answer is:
attracts
'invites' is the definition.
The definition and answer can be both to do with contact as well as being verbs in their -s form.
Maybe they are linked in a way I don't understand?
I don't understand the rest of the clue.
Can you help me to learn more?
(Other definitions for attracts that I've seen before include "Draws, pulls in" , "Draws towards as magnet does iron" , "Draws attention to" , "Has a magnetic effect" , "Exerts a force, draws" .)