I'm left out of bible reading, so have a drink (6)
I believe the answer is:
imbibe
'have a drink' is the definition.
(I've seen this in another clue)
'i'm left out of bible' is the wordplay.
'left' becomes 'L' (common abbreviation).
'out of' indicates named letters should be taken away.
'bible' with 'l' removed is 'bibe'.
'im'+'bibe'='IMBIBE'
'reading so' is the 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 imbibe that I've seen before include "Take in (with one's mother's milk?)" , "Drink or absorb into mind" , "Drink, take in" , "Partake of drink" , "Swallow" .)