  Recently, new debates about the role of layers of strong shear have emerged
in stellar dynamo theory. Further information on the long-term magnetic
activity of fully convective stars could help determine whether their
underlying dynamo could sustain activity cycles similar to the solar one.
  We performed a thorough study of the short- and long-term magnetic activity
of the young active dM4 star Gl 729. First, we analyzed long-cadence $K2$
photometry to characterize its transient events (e.g., flares) and global and
surface differential rotation. Then, from the Mount Wilson $S$-indexes derived
from CASLEO spectra and other public observations, we analyzed its long-term
activity between 1998 and 2020 with four different time-domain techniques to
detect cyclic patterns. Finally, we explored the chromospheric activity at
different heights with simultaneous measurements of the H$\alpha$ and the Na I
D indexes, and we analyzed their relations with the $S$-Index.
  We found that the cumulative flare frequency follows a power-law distribution
with slope $\sim- 0.73$ for the range $10^{32}$ to $10^{34}$ erg. We obtained
$P_{rot} = (2.848 \pm 0.001)$ days, and we found no evidence of differential
rotation. We also found that this young active star presents a long-term
activity cycle with a length of $\text{about four}$ years; there is less
significant evidence of a shorter cycle of $0.8$ year. The star also shows a
broad activity minimum between 1998 and 2004. We found a correlation between
the S index, on the one hand, and the H$\alpha$ the Na I D indexes, on the
other hand, although the saturation level of these last two indexes is not
observed in the Ca lines.
  Because the maximum-entropy spot model does not reflect migration between
active longitudes, this activity cycle cannot be explained by a solar-type
dynamo. It is probably caused by an $\alpha^2$-dynamo.
