Overexpression of telomerase incites the abnormal proliferation of cancer cells. Thus, it has been regarded as a cancer biomarker and a potential therapeutic target. Existing assays suggest a promising sensing scheme to detect telomerase activity. However, they are complicated in terms of assay preparation and implementation. We herein report a Quenching-Exempt invader Signal Amplification Test, termed 'QUEST'. The assay leverages on a high turnover, specific cleaving enzyme, flap endonuclease I (FEN1), and graphene oxide (GO) for background (BG) filtering. In response to the target, FEN1 significantly boosts the signal with invader signal amplification. To distinguish the target signal, GO filters out the BG. It captures residual reporter invader probes (RP) to quench undesired signals. QUEST is straightforward without any pre-preparatory steps and washing/separation. Its probe design is simple and cost-effective. With QUEST, we investigated telomerase activities in various cell lines. Notably, we discriminated cancer cell lines from normal cell lines. In addition, a candidate inhibitor for telomerase was screened, which showed the promising potential of QUEST in real applications.