How old is the Doctor at the end of The Time of The Doctor?

In The Time of The Doctor, the Doctor curses the TARDIS for being missing for 300 years when he was on Trenzalore protecting the people of Christmas. So now is the Doctor 1500 years old?

Answer

1,500 is a conservative estimate.

If we assume that Eleven's count is accurate (see below), then yes: 1,500 years seems like a good rough estimate of his minimum current age.

However, it's hard to tell how long Clara was absent the second time she got sent away; it was probably at least a generation, but could possibly have been only a few minutes. So let's say he's most likely 1,500+ years old, with a lot of wiggle room either way for "I can't remember if I'm lying about my age."

The show is being deliberately hard to pin down about this.

The Doctor's age fluctuates wildly.

The Second Doctor claimed his age was everywhere from 450 to "several thousand" years; the Fourth Doctor got called out for lying about his age; Seven he admitted he'd possibly lost count; Nine evaded the issue by talking about how many years he'd been flying the TARDIS (which doesn't match anyone else's numbers anyway); Ten said he was younger than Seven had; and Eleven can't remember if he's lying about it or not (which neatly circumvents Christmas's truth field)!

Moffat (Eleven's producer and head script writer) has gone on record saying he's operating on the notion that any number the Doctor gives is at best an educated guess:

The thing I keep banging on about is that he doesn't know what age he is. He's lying. How could he know, unless he's marking it on a wall? He could be 8,000 years old, he could be a million. He has no clue. The calendar will give him no clues.

So... sure, let's say 1,500, with a nod and wink.