The most common and most likely answer to this crossword clue is the 7 letter word TRUDGED
I've seen this crossword clue in The Daily Telegraph
T
R
U
D
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More clues leading to the result TRUDGED
Buddy explains!

The straight part
We know that "Had a tramp" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case had a tramp = trudged.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 TRUDGED mean?
TRUDGED verb- To walk wearily with heavy, slow steps.
- To trudge along or over a route etc.