The most common and most likely answer to this crossword clue is the 8 letter word FEASTING
I've seen this crossword clue in The Daily Telegraph
F
E
A
S
T
I
N
G
Buddy explains!

The straight part
We know that "eating heartily" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case eating heartily = feasting.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does FEASTING mean?
FEASTING verb- To partake in a feast, or large meal.
- To dwell upon (something) with delight.
- To hold a feast in honor of (someone).
- To serve as a feast for; to feed sumptuously.
- A feast, or an occasion on which people or animals feast