  We present the results of a high-cadence photometric survey of an
$11'\times11'$ field centred on the globular cluster M71, with the
Near-Infrared Transiting ExoplanetS Telescope. The aim of our survey is to
search for stellar variability and transiting giant exoplanets. This survey
differs from previous photometric surveys of M71 in that it is more sensitive
to lower amplitude ($\Delta M\leq0.02$ mag) and longer period ($P>2$ d)
variability than previous work on this cluster. We have discovered $17$ new
variable stars towards M71 and confirm the nature of $13$ previously known
objects, for which the orbital periods of $7$ are refined or newly determined.
Given the photometric precision of our high-cadence survey on the horizontal
branch of M71, we confirm the cluster is devoid of RR Lyrae variable stars
within the area surveyed. We present new $B$ and $V$ band photometry of the
stars in our sample from which we estimate spectral types of the variable
objects. We also search our survey data for transiting hot Jupiters and present
simulations of the expected number of detections. Approximately $1\,000$ stars
were observed on the main-sequence of M71 with sufficient photometric accuracy
to detect a transiting hot Jupiter, however none were found.
