What I've done in between headshots, is I've gone to auditions with my old ones and a little 4x6 or 5x7 computer print out of my new headshot attached to it. Most of us have the files of our new headshots now...It's not like the old days of film...Anyway, I will also put a little note saying that my new headshot is being printed and coming soon.
And if I have the opportunity, I mention it briefly to who I am auditioning for.
For mailed submission I do the same thing: attach a smaller version of new headshot to old one with a note.
This has worked fine for me and has never kept me from getting an audition, call back or job.
Casting directors appreciate your effort, honesty and professionalism. It's no big deal. People get new headshots all the time and there is a lag time in between.
"You ask my advice about acting? Speak clearly, don't bump into the furniture and if you must have motivation, think of your pay packet on Friday." Noel Coward.