Transposable element (TE) mobilization is a constant threat to genome integrity. Eukaryotic organisms have evolved robust defensive mechanisms to suppress their activity, yet TEs can escape suppression and proliferate, creating strong selective pressure for host defense to adapt. This genomic conflict fuels a never-ending arms race that drives the rapid evolution of TEs and recurrent positive selection of genes involved in host defense; the latter has been shown to contribute to postzygotic hybrid incompatibility. However, how TE proliferation impacts genome and regulatory divergence remains poorly understood. Here, we report the highly complete and contiguous (N50 = 33.8–38.0 Mb) genome assemblies of seven closely related Drosophila species that belong to the nasuta species group—a poorly studied group of flies that radiated in the last 2 My. We constructed a high-quality de novo TE library and gathered germline RNA-seq data, which allowed us to comprehensively annotate and compare TE insertion patterns between the species, and infer the evolutionary forces controlling their spread. We find a strong negative association between TE insertion frequency and expression of genes nearby; this likely reflects survivor bias from reduced fitness impact of TEs inserting near lowly expressed, nonessential genes, with limited TE-induced epigenetic silencing. Phylogenetic analyses of insertions of 147 TE families reveal that 53% of them show recent amplification in at least one species. The most highly amplified TE is a nonautonomous DNA element (Drosophila INterspersed Element; DINE) which has gone through multiple bouts of expansions with thousands of full-length copies littered throughout each genome. Across all TEs, we find that TEs expansions are significantly associated with high expression in the expanded species consistent with suppression escape. Thus, whereas horizontal transfer followed by the invasion of a naïve genome has been highlighted to explain the long-term survival of TEs, our analysis suggests that evasion of host suppression of resident TEs is a major strategy to persist over evolutionary times. Altogether, our results shed light on the heterogenous and context-dependent nature in which TEs affect gene regulation and the dynamics of rampant TE proliferation amidst a recently radiated species group.