  The next generation of TeV detectors is expected to have a significantly
enhanced performance. It is therefore constructive to search for new TeV
candidates for observation. This paper focuses on TeV candidates among the
high-synchrotron-peaked BL Lacertae objects (HBLs) reported in the fourth
catalog of active galactic nuclei detected by the Fermi's Large Area Telescope,
i.e., 4LAC. By cross-matching the Fermi data with radio and optical
observations, we collected the multiwavelength features of 180 HBLs with known
redshift. The data set contains 39 confirmed TeV sources and 141 objects whose
TeV detection has not yet been reported (either not yet observed, or observed
but not detected). Using two kinds of supervised machine-learning (SML)
methods, we searched for new possible TeV candidates (PTCs) among the
nondetected objects by assessing the similarity of their multi-wavelength
properties to existing TeV-detected objects. The classification results of the
two SML classifiers were combined and the 24 highest-confidence PTCs were
proposed as the best candidates. We calculate, here, the 12 year averaged Fermi
spectra of these PTCs and estimate their detectability by extrapolating the
Fermi spectrum and including the extragalactic background light attenuation.
Four candidates are suggested to have a high likelihood of being detected by
the Large High Altitude Air Shower Observatory and 24 are candidates for the
Cerenkov Telescope Array observations.
