Risk compensation is the technical term for the general phenomenon of people engaging in riskier behaviour because they feel safer. Searching for "PrEP and risk compensation" on PubMed and digging through a bit: the answer seems to be "there is some evidence for a decrease in condom use/increase in condomless sex with PrEP, but it's not very consistent; the answer depends on the metric you use" (e.g., MSM who already had some condomless sex tended to have more condomless sex [reducing the frequency of condom use, or having more partners] under PrEP, but the proportion of MSM who had any condomless sex did not increase significantly).
From Quaife et al. 2020: no evidence of change in condom use when recipients only knew that they might be getting PrEP (i.e., "placebo-controlled" studies), but some evidence that MSM had more condomless sex in "open-label" studies:
Self-reported condom use and STIs did not change in
placebo-controlled PrEP studies.3,8 However, in some
open-label studies in which users knew they were
taking highly effective PrEP, its use was associated with
an increase in condomless sex and, most importantly,
STIs.9 One observational study showed evidence of risk
compensation at the community level, whereby even
MSM who were not using PrEP reduced their condom use
as overall PrEP coverage increased.10 Six presentations at
the 2018 International AIDS Conference in Amsterdam
(appendix) provided further, valuable evidence of risk
compensation.
In Traeger et al. (2018), which is reference 9 from the paragraph above, the authors did a formal meta-analysis of incidence of STIs in PrEP trials and found overall that the incidence of STIs (other than HIVs) indeed increased with PrEP treatment, although not quite significantly at the p<0.05 level (odds ratio of 1.24, 95% CI 0.99 - 1.54). Their bottom line conclusion about sexual behaviour was:
Although changes in self-reported sexual risk behavior varied across study populations, most instances reflected an increased number of different condomless partners or a decrease in overall condom use, rather than a change in proportion of men engaging in any condomless sex. ... These findings suggest that risk compensation is most prominent among MSM already engaging in behaviors that place them at risk of HIV and support risk-based guidelines for PrEP [10].
A longer discussion:
None of the studies found a significant increase in the proportion of MSM reporting any condomless sex from baseline to follow-up. However, across studies there was evidence of an increased proportion of participants reporting condomless receptive anal sex with ≥10 partners [35], condomless sex with an HIV-positive or HIV-unknown partner [36, 41], and never using condoms during anal sex [37]. Only 1 study reported a significant decrease in the proportion reporting condomless receptive sex over time; however, this study was the first open-label PrEP study, and findings may reflect the effectiveness of safe-sex counseling prior to later PrEP normalization. There was also no difference in change in condom use between PrEP and non-PrEP arms in this study [29]. Longitudinal modeling adjusting for age and ethnicity found an increase in the mean number of condomless anal sex partners among MSM in a US cohort from baseline to 6 months but no change in total number of partners, suggesting a decrease in condom use over time [38]. An Australian demonstration project found a decrease in frequency of condom use with regular and casual partners over 1 year of follow-up among cohort participants [32]. Two studies reported decreased condom use among 25%–41% of study participants [39, 40].
If you want the full story you can read their detailed table 3, which gives the detailed results from 17 studies of PrEP and sexual behaviour.
Quaife, Matthew, Louis MacGregor, Jason J. Ong, Mitzy Gafos, Sergio Torres-Rueda, Hannah Grant, Fern Terris-Prestholt, and Peter Vickerman. 2020. “Risk Compensation and STI Incidence in PrEP Programmes.” The Lancet. HIV 7 (4): e222–23. https://doi.org/10.1016/S2352-3018(19)30333-9.
Traeger, Michael W, Sophia E Schroeder, Edwina J Wright, Margaret E Hellard, Vincent J Cornelisse, Joseph S Doyle, and Mark A Stoové. 2018. “Effects of Pre-Exposure Prophylaxis for the Prevention of Human Immunodeficiency Virus Infection on Sexual Risk Behavior in Men Who Have Sex With Men: A Systematic Review and Meta-Analysis.” Clinical Infectious Diseases 67 (5): 676–86. https://doi.org/10.1093/cid/ciy182.
