In the season 3 finale, The Master suppressed the regeneration ability of 10th Doctor and increased his age to 900 years which made him a Gollum-like creature.
From Last of the Time Lords episode transcript:
MASTER: What if I suspend your capacity to regenerate? All nine hundred years of your life, Doctor. What if we could see them?
(The Master retunes his screwdriver and zaps the Doctor again.)
MASTER: Older and older and older. Down you go, Doctor. Down, down, down the years.
(Finally the convulsions end. The Doctor is no longer sitting in the wheelchair.)
(A tiny creature with big eyes, rather Gollum-like, peers out from the otherwise empty clothes.)
At old age, The Doctor regenerates (like The War Doctor), but this time his generation ability was suppressed. So, the situation was just like 11th Doctor in The Time of The Doctor when he didn't have regeneration energy to regenerate. In The Time of The Doctor, when The Doctor was going to die of old age (after living probably 900 years), he wasn't Gollum-like creature.
If I am asking in chronologically wrong order, the question may be: Why didn't The Doctor turn into Gollum-like creature in The Time of The Doctor?