I am using a construct that does not have a TEV cleavage site between my protein and the 6xHIS tag, and I was wondering if I could use Q5 site directed mutagenesis kit to insert it or would I need to order a new construct?
No need to buy expensive kits, Quick-Change style site directed mutagenesis should work. Just get suitable primers, Dpn I, a non-proofreading polymerase, and use a methylating E. coli strain.
Important: Sequence some clones or do a functional assay (TEV cleavage) of the modified protein, if you may spot the difference in size on SDS PAGE.
Depending on your sequence (availability of restriction sites), you also may use adapter primers for introducing the site by PCR.
You can insert it by insertional mutagenesis. But, I recommend just ordering primer for conventional PCR (with TEV seq and restriction sites) and cloning your desired seq in any of your desired vectors.
You don't even need to include restriction site in your primers. Just design primers spanning the site where you want to include your TEV cleavage site and the TEV cleavage site (optionally with some more nt at the other side of the TEV cleavage site, if the overlap is short). Do PCR; DpnI treatment; transform.
you can use PIPE cloning, which is similar to the site directed mutagenesys.
You need just an hifgh fidelity polimerase as KApa Hifi or Clone Amp and E.coli Mach1 cells and desing primers with overlapping regions those contain the TEV site:
you can find more details about pipe cloning on my blog at the following link