The most common and most likely answer to this crossword clue is the 6 letter word SKINNY
I've seen this crossword clue in The Times
S
K
I
N
N
Y
More clues leading to the result SKINNY
- Hotel where there may be pie? But without fat
- Pub in elevated region having had little in the way of food?
- Lean out of empty shack in New York
- Spare sauce but no dressing for this
- Go crawling along out of gear?
- Fashionable new blue clothes and kid’s tight sweater
- . Diet of family in South American city
- Pub invested in satellite TV, not doing enough food
- Thin broadcaster coverage of pub
- Tight-fitting blue clothes in Norway
Buddy explains!

The straight part
We know that "having had little in the way of food" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case having had little in the way of food = skinny.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 SKINNY mean?
SKINNY noun- The details or facts; especially, those obtained by gossip or rumor.
- A state of nakedness; nudity.
- A low-fat serving of coffee.
- A skinny being.
- To reduce or cut down.
- Thin, generally in a negative sense (as opposed to slim, which is thin in a positive sense).
- (of food or beverages) Low-fat.
- Naked; nude (chiefly used in the phrase skinny dipping).
- (of clothing) tight-fitting