The most common and most likely answer to this crossword clue is the 4 plus 3 letter word TICK OFF
T
I
C
K
O
F
F
More clues leading to the result TICK OFF
- Hire purchase no longer available for carpet
- Rebuke coming from country bumpkin losing head, interrupting smart gent
- Absence of credit bringing reprimand
- Lecture Mark completed
- I'm disgusted, aristocrat admits, to dress down
- Reprimand for bad mark earlier
- Departing after second lecture
- Mark items individually for lecture
- Mark wrong in lecture
- Mark in carpet
Buddy explains!

The straight part
We know that "Systematically check/anger" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case systematically check/anger = tick off.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.