Host "A" has only Template 1 attached to it. And was pooling data according to it.
Unlink Template 1 from Host "A".
Attach and Save Template 2 to Host "A".

Expected : New items will be discovered by LLD in Template 2, Host will poll for values of these new items.
Observed : Items discovered by LLD in template 1 keep on being polled, No new items discovered by LLD in Template 2.

PS: Both templates contain 1 LLD rule.
Key of LLD in Template 1 = xyz[Basic]
Key of LLD in Template 2 = xyz[Advance]