Vessel has influence with a lot of doctors outside (7)
I believe the answer is:
ampulla
'vessel' is the definition.
(ampulla is a kind of vessel)
'with a lot of doctors outside' is the wordplay.
'with' says to put letters next to each other.
'a' becomes 'amp' (A is the symbol for the amp or ampere).
'lot of doctors outside' becomes 'ulla' (I can't explain this - if you can you should give a lot more credence to this answer).
'amp' next to 'ulla' is 'AMPULLA'.
'has influence' acts as a link.
I am not very happy about this link. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for ampulla that I've seen before include "Ancient Roman flask" , "Sacred vessel" , "Container for wine and water in church" .)