Let's consider the Mean Square Error of an approximation of a parameter $$\theta$$ by $$\hat{\theta}$$.
$$\mathbb{E}(\theta-\hat{\theta})^2=Var(\hat{\theta})+(Bias(\hat{\theta}))^{2}$$
Absolutely! So when you say "increase", I assume you start from some baseline estimator. Say you have a i.i.d. sample $$X_1, ..., X_n$$ and want to find the mean $$\theta = E[X]$$. Your baseline estimator is the sample mean $$\hat{\theta} = \frac{1}{n} \sum_{i=1}^n X_i$$.
Recall that you can make any unbiased estimator biased by simply adding some constant $$c \neq 0$$. Now consider the estimator $$\tilde{\theta} = X_1 + 1$$. It should be clear that $$\tilde{\theta}$$ has both a larger variance than $$\hat{\theta}$$ and is also biased now.