I have a question:
I have a question:
“挾怨報復”：心懷怨恨而報仇（bear resentment against somebody and retaliate）。
This is indeed a very common word. But most of the dictionaries list only "挾嫌報復" which has the same meaning.
If the predecessor is very picky or deliberately twists your reports, you do be able to use this term.
“一朝權在手，便把令來行”：一旦握有權勢，便下命令。(Once the ascendancy is held, the commands are given.)
There is only one point related to the situation; i.e., because of being a senior, he is more powerful.
But this sentence doesn't mean "deliberately looking for trouble (revenge)".
"便把令來行" is not necessarily related to revenge.
"心胸狹窄，倚勢挾權": These two phrases together mean that "a narrow-minded person abuses the privilege".
There are two aspects related to the case.
1. You corrected his reports, but he couldn't tolerate. It's connected with "心胸狹窄".
2. He takes advantage of the power of a predecessor.
This sentence implies "revenge" a little, but less obvious.
“倚老賣老”：賣弄老資格 (to flaunt one's seniority)。
This is relevant only to that "he is a predecessor".
“竊弄威權”：暗地裡玩弄權勢 (to abuse authority secretly)。
This is related to that "he uses the power of a predecessor".
Comparison of these words, "挾怨報復／挾嫌報復" is still more applicable.
According to your description, your senior fellow employee showed he has a temperament of 「刚愎自用」(self-willed), 「心胸狭窄」(narrow-minded) and 「不容异已」(intolerance to opinion different from his own).
And his motives can be described as 「记仇」(vengeful).
As for the act itself, it can be said to be 「恶意刁难」(maliciously seeking trouble for others)
「刚愎自用」(self-willed) : always thought he must be right, bent on resisting all the different views.
「心胸狭窄」(narrow-minded): never forgive
「不容异已」(intolerance of views different from his own): stubbornly ruled out all opponents
「记仇」(Vengeful): always hold grudge
「恶意刁难」(maliciously seek trouble for others)
I have never heard of 挟怨报复 as an idiom,
挟怨 can be translated to "hold a grudge"
报复 means "revenge"
挟怨报复 means "hold a grudge and seek revenge"