Verb review may serve. You might also use the circumlocution perform oversight which is (I think) jargon for “inspect the work of”. Double-check is another possibility.
Note that review is quite a broad term; but in the workplace, if you say you will review work a person has done, that typically implies you are in a supervisory role relative to that person, and will inspect their work for correctness, timeliness, etc., in more or less detail depending on circumstances. In a programming environment and in some technical environments, review often connotes code review or design review:
Code review is systematic examination (often known as peer review) of computer source code. It is intended to find and fix mistakes overlooked in the initial development phase, improving both the overall quality of software and the developers' skills. Reviews are done in various forms such as pair programming, informal walkthroughs, and formal inspections.
A design review is a milestone within a product development process whereby a design is evaluated against its requirements ... to verify the outcomes of previous activities ... The ultimate design review, if successful, ... triggers the product launch or product release.
In these contexts, review connotes careful examination, and says nothing about whether the reviewer has looked at the subject before.
As noted above, perform oversight is jargon; eg
The Department of Energy (DoE) remedial site activities are handled by three empowered work teams that perform oversight function to the DoE sites – [a Region 4
However, the ability of the intelligence committees to perform oversight of the intelligence agencies and account for their performance is still undermined... – [a Better Government | Congressional Reform webpage]
Being in a position to perform oversight indicates that the agent (the inspector) has the power to make a decision after reviewing work, and to say whether that work is satisfactory.