If you want the whipped egg whites to turn out properly and if your goal is to beat the egg whites to a stiff meringue then yes you need cream of tarter.
You need the cream of tarter along with lemon juice to be able to beat the egg whites to a stiff meringue.
If you do not use cream of tarter and lemon juice when beating the egg whites then the egg whites will not beat to the stiff meringue.
However if you just want to beat the egg whites and don't need them to be beat to a stiff meringue then you don't need the cream of tarter or lemon juice.
The cream of tarter and lemon juice is only required and needed when beating your egg whites to a stiff meringue.