Do you really want to compute a new TLE, or just a new orbit? The TLE format itself is a significant problem, so it's best to avoid if possible. If you just need to look for changes in the orbit state, you should use SGP4 to convert into position and velocity, propagate the state with and without the maneuver using something other than SGP4, and convert each of those to some orbital elements that aren't the excessively complicated mean elements used for TLEs.
If you are committed to TLE generation, I must reaffirm uhoh's answer of please don't do this, especially the part that says "There is nothing involved in doing a better job now that would be harder than understanding the process that is used to determine the parameters in TLEs that give the best results when interpreted through SGP4."
If your delta-V is small enough, then the change may be less than the error built into the TLE itself, which is on the order of several kilometers and several meters per second. Only use TLEs if you have no other source of data available.
The only guaranteed way to compute a new, self-consistent TLE is to use the same software the US Air Force did to compute the original TLE in the first place. This is possible if you are engaged in official business for the US government on an approved contract, but even they don't get to see the real data from which the TLE (or the other format they actually distribute to the people who have completed the official approval process) was created.
I stress needing to use the USAF batch differential corrector because there are several important fields in the TLE that don't exist in any other format, and only the official software knows how to compute those extra terms. I'm talking partly about the derivatives of the mean motion, but mainly the problem is the "B star" term. Most references on the internet give a formula for calculating the atmospheric drag, but that is only the starting point. The actual value appearing in the TLE is not the result of that formula, because it is used by the orbit determination process as a dumping ground for lots of other effects which are not modeled well (or at all) by SGP4. There is a wonderful footnote in Vallado's Fundamentals of Astrodynamics and Applications (page 106 in the 4th edition), which says:
Be aware that the value of B* is always modified. It’s really an
arbitrary free parameter in differential correction. Chapter 10 will
introduce how to estimate a drag parameter. The estimated value of B*
may be completely unrelated to drag effects in the presence of
satellite maneuvers, significant solar pressure and atmospheric
perturbations, large third-body effects from the Sun or Moon, or large
deflections caused by mismodeling of the Earth’s gravitational field.
B* can even appear as a negative number!
Even people who do have access to all the right tools struggle with this, as in this master's thesis from the Air Force Institute of Technology.