Executives world-wide are on the move again—and rental prices are rising to the occasion.

The upswing includes places that haven’t seen such surges before. New sectors are expanding into emerging markets—like the automobile industry in Shanghai, and accounting and law in Hong Kong—and sparking demand for high-end rentals, as weak European economies force companies to look elsewhere for business.

Four cities that have seen some of the biggest jumps in rental prices over the past year are Dubai, where an apartment in a prime location surged 14.3% from 2012 to $3,628 a month for a two-bedroom; Beijing, up 8.5% to $3,125 a month; Shanghai, up 6.1% to $3,387; and Hong Kong, up 3.7% to $6,223, according to Knight Frank, a global property consultancy based in London.

Expat living, on the whole, seems to be on the rise, with global rents jumping 5.1% over the past year in 11 global cities surveyed. New York City grew a relatively modest 4.5% but has the highest monthly rent—roughly $8,200 a month—of the cities surveyed.

Knight Frank’s latest Global Corporate Lettings Review looked at prime rental demand in the 11 cities, largely based on expatriate demand. Knight Frank surveyed its teams world-wide to see what properties and amenities are most often requested by corporate executives working abroad, and what price is “typical” for the area. The report is scheduled to be released Friday.

Corporate accommodations account for up to 85% of prime apartments in some cities, said Kate Everett-Allen, international residential analyst at Knight Frank, who worked on the report.

“We saw a big drop-off in [human resources] budgets post-2008. Now that’s starting to come back, but it’s coming back stronger in these emerging markets as opposed to traditional markets,” she said.

For expats, ease of living is key. Roughly 90% of corporate staffers in Shanghai and 100% in Beijing request furnished units, according to the report. In New York, only 10% ask for furnished units. Ultraluxurious amenities sometimes outrank other factors, such as location or size, says Josh Doyle, senior vice president and associate broker at Corcoran.

Mr. Doyle recently worked with a Vancouver, British Columbia, couple who had to relocate to New York City for work. At first, they looked in neighborhoods downtown to be close to their office. Eventually they settled in a $13,000-a-month, two-bedroom apartment in midtown—drawn to more than 44,000 square feet of amenities offered by One MiMA Tower, the luxury rental residences on West 42nd Street.

Last year, the first year Knight Frank released this report, Shanghai saw the biggest year-to-year increase in rental prices, at 8.2%.

This year, Dubai showed the most growth.

“Downtown Dubai has matured quite a lot over the past 18 months,” Ms. Everett-Allen said. “Location is pretty much key.”