We use Gaia DR3 astrometry and photometry to analyze the spatial distribution of the young stellar populations and stellar clusters, and to search for new OB star candidates in the Carina Nebula Complex and the full extent (~5{deg}, corresponding to ~200pc) of the Car OB1 association. First, we perform a new census of high-mass stars in Car OB1 and compile a comprehensive catalog of 517 stars with known spectral types (128 O-type, WR, and supergiant stars, and 389 B-type stars) which have Gaia DR3 parallaxes consistent with membership in the association. We apply the clustering algorithm DBSCAN on the Gaia DR3 data of the region to find stellar clusters, determine their distances and kinematics, and estimate ages. We also use Gaia astrometry and the additional astrophysical_parameterstable to perform a spatially unbiased search for further high-mass members of Car OB1 over the full area of the association. Our DBSCAN analysis finds 15 stellar clusters and groups in Car OB1, four of which were not known before. Most clusters (80%) show signs of expansion/contraction, four of them with >2{sigma} significance. We find a global expansion of the Car OB1 association with a velocity of v_out_=5.25+/-0.02km/s. A kinematic traceback of the high-mass stars shows that the spatial extent of the association was at a minimum 3-4 Myr ago. Using astrophysical parameters by Gaia DR3, we identify 15 new O-type and 589 new B-type star candidates in Car OB1. The majority (>54%) of the high-mass stars constitutes a non-clustered, distributed stellar population. Based on our sample of high-mass stars we estimate a total stellar population of at least ~8*10^4^stars in Car OB1. Our study is the first systematic astrometric analysis that covers the full spatial extent of the Car OB1 association, and therefore substantially increases the knowledge of the distributed stellar population and spatial evolution of the whole association. It suggests Car OB1 to be the most massive known star-forming complex in our Galaxy.