Amnesia is a great story-telling trait that is not specifically addressed in the WFRP 2e RAW (the word does not appear in the Core Rulebook or Tome of Corruption--where I might expect it to appear as result of a mutation).
As GM, you should not restrict the player's Starting, Advance or Current Profile. However, Skills represent that player's ability to perform something that the Amnesia would effectively block.
As the player, real world Amnesia can take on many forms and "depths"--for instance most do not forget vocabulary or language skills, but forget personal things. Wikipedia is one source for the player to use in building character depth (though should not be considered clinical research).
These two things should be worked out by the player and the GM before the campaign is too far along, first or second session.
Mechanically, here are some things I might do as a GM—assuming a general amnesia that wipes personal experience and mid-term memories like work skills, name, familiar relationships, etc.:
Force all Basic skill rolls as unskilled (1/2
characteristic) for a predetermined number of tries, e.g., 5
attempts, each attempt incrementally improving the roll by some %
to full ability.
For Advanced Skills that require learning, I would force the
player to devise story elements to remember them. Further, I might
restrict access to them entirely without succeeding a Hard (-20%) or
Very Hard (-30%) WP or Int test (or maybe spending a Fate point if
the amnesia is really deep!) and providing a story element to
use, e.g., Swim... the player is pushed into the sewer by the Skaven
slave: does he drown? spend a Fate point? succeed a test? remember
teaching a small child (son/daughter?) how to fetch a turtle? Force
a story from the player and adjust the difficulty accordingly, maybe
requiring a number of attempts before fully accessing the Advanced
Talents? Night Vision is something he/she has naturally. Each talent
may require some work in the character background.
Now, advancement, learning new skills, etc. Play that as RAW, unless there is a prerequisite that is expected. The character is not beyond learning new things, so normal XP advancement should be allowed. Maybe remove the XP cost (200XP) for jumping careers (one time only). After all, the PC doesn't really know why he/she is good at one thing and could just as well do this "other" thing.
Amnesia is going to be a big flavor and story element in the PC and game. Don't let the PC forget it either (pun intended!). At some point the amnesia may be magically healed or overcome, decide up front with the player what that expectation is and when it might happen in the character's arc.