The ability of species to track their climate niche is dependent on their dispersal potential and the connectivity of the landscape matrix linking current and future suitable habitat. However, studies modeling climate-driven range shifts rarely address the movement of species across landscapes realistically, often assuming “unlimited” or “no” dispersal. Here, we incorporate dispersal rate and landscape connectivity with a species distribution model (Maxent) to assess the extent to which the Cunningham’s skink (Egernia cunninghami) may be capable of tracking spatial shifts in suitable habitat as climate changes. Our model was projected onto four contrasting, but equally plausible, scenarios describing futures that are (relative to now) hot/wet, warm/dry, hot/with similar precipitation and warm/wet, at six time horizons with decadal intervals (2020–2070) and at two spatial resolutions: 1 km and 250 m. The size of suitable habitat was projected to decline 23–63% at 1 km and 26–64% at 250 m, by 2070. Combining Maxent output with the dispersal rate of the species and connectivity of the intervening landscape matrix showed that most current populations in regions projected to become unsuitable in the medium to long term, will be unable to shift the distance necessary to reach suitable habitat. In particular, numerous populations currently inhabiting the trailing edge of the species’ range are highly unlikely to be able to disperse fast enough to track climate change. Unless these populations are capable of adaptation they are likely to be extirpated. We note, however, that the core of the species distribution remains suitable across the broad spectrum of climate scenarios considered. Our findings highlight challenges faced by philopatric species and the importance of adaptation for the persistence of peripheral populations under climate change.