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 4 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: MAa = 3.58 ± 0.11, MAb = 1.68 ± 0.09 (M⊙); RAa = 2.17 ± 0.03, RAb = 1.51 ± 0.06 (R⊙), and TeAa = 13300 ± 500, TeAb = 7400 ± 500 (K). We estimate approximate masses of the wide companions, Ba and Bb, as MBa = 2.0 and MBb = 1.8 (M⊙). The close binary’s orbital separation is a = 8.51 ± 0.05 (R⊙); its age is approximately 20 Myr and distance 172 ± 1 pc. The close binary’s secondary (Ab) appears to be the source of low amplitude δ Scuti-type oscillations, although the form of these oscillations is irregular and unrepetitive. Analysis of the λ 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.