The most common and most likely answer to this crossword clue is the 7 letter word INROADS
I've seen this crossword clue in Independent
I
N
R
O
A
D
S
More clues leading to the result INROADS
- Attacks trendy bars, penning article
- Way to stop nearly half of 20’s hostile attacks
- Progress with play, mostly sardonic
- These incursions not cross-country?
- Raids in Mediterranean island reported
- Batting first, sounds like Cecil is making some headway
- Lunatic half-responds with air raids
- What invaders hope to make
- Outgoing raids? No
- Hostile incursions into Greek island, say?
Buddy explains!

The straight part
We know that "some headway" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case some headway = inroads.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 INROADS mean?
INROADS noun- An advance into enemy territory, an incursion, an attempted invasion
- (usually plural) progress made toward accomplishing a goal or solving a problem