When I renewed over 5 years ago, I got a letter from the PD about six months before hand advising me to renew soon. When I met with the detective, he told me they were sending out all the renewals at the end of the week and I should expect it to take about 12 weeks to get my new card. Twelve weeks to the day, I had my new license. I got it about two months before my birthday, but the issue date was on my birthday, when my prior license expired. This was also right after Sandy Hook though so they were pretty backed up. Now that the frenzy over that has died down, I wouldn't expect it to take as long, but anyone who applied/renewed at that time is coming up for renewal now, so it may be the same situation.
That also reminds me that I'll have to start the renewal process later this year.