  We present the first study of collectivity inside jets with high charged
multiplicity $N^j_{\rm ch}$ in proton-proton collisions at the Large Hadron
Collider. By incorporating final-state partonic and hadronic interactions
through cascade models among jet shower partons and final hadrons, we
investigate and compare to the CMS experimental data on multiplicity
distribution, pseudorapidity distribution, and elliptic anisotropy coefficient
$v^{j}_2$ of two-particle correlations within the jet. We show that final-state
partonic interactions are essential for producing the flow-like long-range
correlation, which leads to the enhanced tail in the $N^j_{\rm ch}$ dependence
of $v^{j}_2$ above the non-flow correlation from jet parton showering at high
multiplicities ($N^j_{\rm ch}\gtrsim70$) as observed in the CMS experimental
data. In addition, we provide predictions for the pseudorapidity-gap dependence
of $v^{j}_2$ that can be tested in future experimental measurements.
