The most common and most likely answer to this crossword clue is the 7 letter word HEADWAY
I've seen this crossword clue in The Guardian
H
E
A
D
W
A
Y
Buddy explains!

The straight part
We know that "Progress" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case progress = headway.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 HEADWAY mean?
HEADWAY noun- Movement ahead or forward.
- Forward motion, or its rate.
- The interval of time or distance between the fronts of two vehicles (e.g. buses) moving in succession in the same direction, especially along the same pre-determined route.
- Progress toward a goal.
- The clearance beneath an object, such as an arch, ceiling or bridge; headroom.
- (coal-mining) A cross-heading.