Old judge to give a lecture (5)
I believe the answer is:
orate
'give a lecture' is the definition.
(I've seen this in another clue)
'old judge' is the wordplay.
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'judge' becomes 'rate' (rating is a kind of judging).
'o'+'rate'='ORATE'
'to' is the link.
(Other definitions for orate that I've seen before include "Spout" , "Speak pompously and at length" , "Speak like Cicero?" , "Harangue" , "Erato (anag.)" .)