Target speaker extraction aims at extracting the target speaker from a mixture of multiple speakers exploiting auxiliary information about the target speaker. In this paper, we consider a complete time-domain target speaker extraction system consisting of a speaker embedder network and a speaker separator network which are jointly trained in an end-to-end learning process. We propose two different architectures for the speaker separator network which are based on the convolutional augmented transformer (conformer). The first architecture uses stacks of conformer and external feed-forward blocks (Conformer-FFN), while the second architecture uses stacks of temporal convolutional network (TCN) and conformer blocks (TCN-Conformer). Experimental results for 2-speaker mixtures, 3-speaker mixtures, and noisy mixtures of 2-speakers show that among the proposed separator networks, the TCN-Conformer significantly improves the target speaker extraction performance compared to the Conformer-FFN and a TCN-based baseline system.