Worldwide, HEIs strive to provide the best possible training for their PGRs, the next generation of researchers. PGRs engagement is crucial for a successful completion of their training, however, research on the experiences of PGRs is limited. Moreover, the number of international PGRs has increased steadily over the last decade, which poses the question whether international PGRs have different engagement levels compared to local PGRs. Therefore, thus study is aimed at filling this research gap by investigating the mechanisms that influence the engagement of these groups of students. The paper focuses on the dimensions of (1) students' engagement with the supervisor, (2) their engagement within the department, and (3) their cognitive engagement, by taking a mixed-method approach that draws on the Irish PGR StudentSurvey.ie 2019 data and 14 semi-structured interviews conducted with PGRs at Trinity College Dublin (TCD) in 2021. The findings indicate that differences in engagement between Irish and international students are mainly influenced by perceived financial security and familiarity with institutional structures and environments, are mediated by their relationship with the supervisor, and ultimately influence the time available for engagement. Therefore, the findings will be relevant to policymakers and HEIs as they offer insights into how challenges for PGR students can be mitigated through supervisor support to encourage higher levels of engagement.