The southern early-type, young, eccentric-orbit eclipsing binary NO Puppis forms the A component of the multiple star Gaia DR3 5528147999779517568. The B component is an astrometric binary now at a separation of about 8.1 arcsec. There may be other fainter stars in this interesting but complex stellar system. We have combined several lines of evidence, including TESS data from four sectors, new ground-based BVR photometry, HARPS (ESO) and HERCULES (UCMJO) high-resolution spectra and astrometry of NO Pup. We derive a revised set of absolute parameters with increased precision. Alternative optimal curve-fitting programs were used in the analysis, allowing a wider view of modelling and parameter uncertainties. The main parameters are as follows: $M_{Aa} = 3.58 \pm 0.11$, $M_{Ab} = 1.68 \pm 0.09$ (M$_\odot$); $R_{Aa} = 2.17 \pm 0.03$, $R_{Ab} = 1.51 \pm 0.06$ (R$_\odot$), and $T_{\mathrm{e Aa}} = 13\,300 \pm 500$, $T_{\mathrm{e Ab}} = 7\,400 \pm 500$ (K). We estimate approximate masses of the wide companions, Ba and Bb, as $M_{Ba} = 2.0$ and $M_{Bb} = 1.8$ (M$_\odot$). The close binary’s orbital separation is $a= 8.51 \pm 0.05$ (R$_\odot$); its age is approximately 20 Myr and distance $172 \pm 1$ pc. The close binary’s secondary (Ab) appears to be the source of low amplitude $ {\delta}$ Scuti-type oscillations, although the form of these oscillations is irregular and unrepetitive. Analysis of the $ \lambda$ 6678 He I profile of the primary show synchronism of the mean bodily and orbital rotations. The retention of significant orbital eccentricity, in view of the closeness of the A-system components, is unexpected and poses challenges for the explanation that we discuss.