For fighters/warriors in general, you get an extra 1/2 attack at the 7th and 13th level. So if you're at level 13, you would already get 2 attacks per round, even when you're using a weapon you're not proficient in.
Weapon Specialization has 5 levels, but apart from the fighter class and its respective kits, the ranger and paladin can only attain at most 2 stars/levels in any particular weapon - Advanced Weapon Specialization. But even so, for this particular weapon, the ranger/paladin should gain an extra 1/2 attack per round.
Note that the above info is applicable to melee weapons - you'll have to refer to the manual for further details (if you haven't in the first place ).
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