The most common and most likely answer to this crossword clue is the 11 letter word GORMANDISED
I've seen this crossword clue in Financial Times
G
O
R
M
A
N
D
I
S
E
D
Buddy explains!

The straight part
We know that "took in eagerly" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case took in eagerly = gormandised.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 GORMANDISED mean?
GORMANDISED verb- To eat food in a gluttonous manner; to gorge; to make a pig of oneself.