The phrase "continue employing" is correct and usable in written English.
It typically means to continue using or hiring someone for a job or task. Here is an example sentence: "We have decided to continue employing John as our project manager for the remainder of the year."
On many occasions he found me asleep at my desk but he was good enough to continue employing me until I was able to have the transplant.
Mr. Clune said new measures would be put in place, and he was reviewing whether or not to continue employing Measurement Incorporated.
Their debts, however, were never large, and they were always able to continue employing servants and owning a carriage; their anxieties were more a matter of whether they could live as they wished than whether they would starve.
This type of contract allows faculty members to continue employing a lab technician based on performance.
The manager of my marketing team and I only wish to continue employing their services under certain conditions.
Whether or not the money gets repaid, it's clear why the organization may not want to continue employing an expense fraudster.
The spouse who is driving the divorce often feels like s/he is being held hostage as the courts crawl along and the spouse who wants the marriage to continue employs various stalling tactics.
Bernini married shortly thereafter, though he continued employing his cuckolded assistant until Matteo's death in 1654.
Its strengthened glass sales have grown to more than $700 million a year, and it has hired or continued employing about 1,000 Americans to support the emerging market.
1980: He continues employing flash effects when he moves to more color work.
1980: He continues employing flash effects when he moves to more color work.
