Deep‐focus earthquakes in the Tonga–Fiji subduction zone make up greater than 66% of the globally recorded deep seismicity. The high number of deep‐focus seismicity in this active subduction zone allows us to search for deep‐focus similar earthquake pairs and repeating earthquakes. We compile a waveform dataset for deep earthquakes with magnitude above 4.7 occurring in the Tonga–Fiji–Kermadec subduction zone recorded teleseismically between 1990 and 2009. We identify 8 similar clusters and 18 similar doublets with an average cross‐correlation coefficient greater than 0.8 among more than 45,000 potential earthquake pairs. These similar doublets and clusters are located in the central part of the Tonga–Fiji slab at the depth range of 480–650 km. A master event relocation algorithm is used to determine the precise relative location and depth among these similar earthquake pairs. We estimate and superpose circular fault areas for these similar clusters and doublets and find that one similar doublet appears to be a deep repeating earthquake pair. This deep doublet has a small separation less than 0.4 km and overlapping rupture areas, indicating that the same fault appears to slip. Other deep similar earthquake pairs are spatially offset or do not exhibit overlapping rupture areas. Time separation is on the order of years for the majority of similar earthquake pairs. Thermal (plastic) shear instability is more likely to explain these deep repeating earthquakes and similar earthquake pairs.