I’ve tried to pull together some of the job market papers featuring trade theory and empirics. I neglect international finance and open economy macro papers here. Feel free to add more in the comments.
Saroj Bhattarai (Princeton) “Optimal Currency Denomination of Trade: Theory and Quantitative Exploration”
Lorenzo Caliendo (Chicago) “Estimates of the Trade and Welfare Effects of NAFTA”
Camila Campos (Yale) “Incomplete Exchange Rate Pass-Through and Extensive Margin of Adjustment”
Arpita Chatterjee (Princeton) “Why Do Similar Countries Choose Different Policies? Endogenous Comparative Advantage, and Welfare Gains”
John Dalton (Minnesota) “Explaining the Growth in Manufacturing Trade”
Swati Dhingra (Madison) “Trading Away Wide Brands for Cheap Brands”
Brian Kovak (Michigan) “Regional Labor Market Effects of Trade Policy: Evidence from Brazilian Liberalization”
Zhiyuan Li (UC Davis) “Task Offshoring and Organizational Form: Theory and Evidence from China”
Lin Lu (Minnesota) “Trade and Variety: The Effect of Within-Country Income Inequality”
Asier Mariscal (Chicago) “Global ownership patterns”
Carlos Noton (Berkeley) “Structural Estimation of Price Adjustment Costs in the European Car Market”
Soonhee Park (Michigan) “International Fragmentation and Work Effort: Networks, Loyalty and Wages”
Ana Maria Santacreu (NYU) “Innovation Diffusion and Trade: Theory and Measurement”
Gloria Sheu (Harvard) “Price, Quality, and Variety: Measuring the Gains from Trade in Differentiated Products”
Victor Shlychkov (Columbia) “Organizational Forms of Importing Firms in U.S. Manufacturing”
Yoichi Sugita (Columbia) “Matching, Quality, and Comparative Advantage: A Unified Theory of Heterogeneous Firm Trade”
John Tang (Berkeley) “Pollution Havens and the Trade in Toxic Chemicals: Evidence from U.S. Trade Flows”
Marc Teignier-Baque (Chicago) “The Role of Trade in Structural Transformation”
Jade Vichyanond (Princeton) “Intellectual Property Protection and Patterns of Trade”
Kevin Wiseman (Minnesota) “Location, productivity, and trade“
Trade Diversion 
Ivan Cherkashin (Penn State) “Firm Heterogeneity and Costly Trade: A New Estimation Strategy and Policy Experiments”
Sohini Chowdhury (Purdue) “The Discriminatory Nature of Specific Tariffs”
Kerem Cosar (Penn State) “Adjusting to Trade Liberalization: Reallocation and Labor Market Policies”
Anca Cristea (Purdue) “Information Transfers in International Trade”
Antoine Gervais (Maryland) “Product Quality and Firm Heterogeneity in International Trade”
Yao Li (Western Ontario) “International Trade, Technology Diffusion, and the Role of Diffusion Barriers”
Jongchol Moon (UCLA) “The Influence of Free Trade Agreement on Foreign Direct Investment”
Piyusha Mutreja (Iowa) “International Trade and Cross-Country Capital Composition Differences”
Laura Puzzello (Purdue) “On the Role of Factor Endowments as a Source of Comparative Advantage”