  This paper addresses inverse spectral problems associated with Dirac-type
operators with a constant delay, specifically when this delay is less than
one-third of the interval length. Our research focuses on eigenvalue behavior
and operator recovery from spectra. We find that two spectra alone are
insufficient to fully recover the potentials. Additionally, we consider the
Ambarzumian-type inverse problem for Dirac-type operators with a delay. Our
results have significant implications for the study of inverse problems related
to the differential operators with a constant delay and may inform future
research directions in this field.
